Formation of the f‐Plane Quasi‐Geostrophic Three‐Dimensional Ocean Circulation Under Wind‐Driven and the Application of Mass Conservation

Abstract

AbstractIn this paper, we divide the idealized South China Sea into Ekman layer, inertial layer and friction layer in the vertical direction. Motions in the Ekman layer are driven by wind stress, and the perturbation pressure on the bottom will be the upper boundary condition of the inertial layer. Motions in the inertial layer are controlled by the potential vorticity conservation derived from the f‐plane three‐dimensional nonlinear equation under quasi‐geostrophic approximation. Then we can get the inertial layer's elliptic control equation, which is about the perturbation pressure. Considering that the horizontal‐scale is small below the inertial layer, we introduce linear control equations with bottom friction. The upper boundary condition of the equations is that the perturbation pressure on the interface of the inertial layer and the friction layer is consistent. Supposing that the seawater has no heat exchange with the solid wall, and then the temperature along the sea basin can be set to zero. From the aboving, we calculated every level's perturbation pressure and quasi‐geostrophic flow by using the ellipse equations in the inertial and friction layer. The results indicate that circulation in each level is cyclonic dominatingly, the velocity decreases with depth, however, there is anti‐cyclonic circulation in summer. It's according with the observation in some degree.